Project Report

Motivation

It’s difficult to overstate the extent to which the COVID-19 pandemic has tested the world’s public health infrastructure over the past two years. At the same time, the COVID-19 “experience” has manifested unequally – not just country to country, but even city to city. As one of the most heterogeneous urban areas in the world, New York City provides a fascinating case study into the ways in which socioeconomic status may be associated with, or even mediate, disparities in health outcomes. (For instance, it’s already well-documented that income and race, along with socioeconomic privilege and political ideology, drive inequities in COVID vaccination rate across US cities.)

Knowing that socioeconomic factors have historically been associated with health outcomes, we aim to examine relationships between a range of predictors (e.g. race/ethnicity, education, broadband internet access, household income / occupational income score, public vs. private health insurance) and COVID-19 health outcomes – namely, hospitalizations, deaths, and vaccinations.

Related Work

In 2020, the COVID-19 pandemic was only one factor that increased the public attention on structural inequality. A confluence of recent events, from the Black Lives Matter movement to the election of New York City’s second Black mayor, has attracted the gaze of local researchers given the vast demographic and socioeconomic diversity concentrated in just one urban area. Our work is motivated by pre-existing analyses related to potential socioeconomic predictors and COVID-19 outcomes. For example, Little et al.’s research suggests an “unequal socioeconomic gradient in the demographic and clinical presentation of COVID-19 patients,” building on other analysis into census tract-level associations with key outcomes like hospitalization. As COVID-19’s endemicity becomes all but inevitable, with globalization expected to contribute to a rise in the number of pandemics easily spread across borders and continents, a comprehensive understanding of the predictors of hospitalization, death, and vaccination rates for COVID-19 may aid the development of effective intervention strategies that limit disparate impact across all disease stages.

While a number of studies have examined differential outcomes across neighborhoods in New York City (and have even, at times, attempted to approach causal explanations, such as subway utilization, no ecological study to-date has explored the potential for a ~20-variable set of predictors to explain between-neighborhood variation across multiple COVID outcomes, including vaccination. Although prior work has explored disparities in testing and positivity, for example – and systemic meta-analyses have demonstrated disparities in COVID-19 outcomes by race, ethnicity, and socioeconomic status – our study takes a modeling-forward approach to generate a multivariate regression model that explains outcomes at the PUMA, or census-tract, level. We also contribute a novel method of predictive risk scoring to highlight the possibility of a given PUMA failing to achieve a key outcome target – in this case, 70% vaccination rate. Although further work will be required to better understand the mechanisms by which various contributing factors are associated with key outcomes, this research highlights the diversity of outcomes across a relatively small geographic area, and thus the potential for greater health equity in the future.

Initial Questions

Our initial questions are centered on how demographic factors in New York City trend with COVID-19 outcomes. Particularly, what are the effects of predictors such as race/ethnicity or education on COVID-19 hospitalizations or vaccinations? Are there differences in COVID-19 hospitalizations or vaccinations when considering public vs. private health insurance? And are there differences in COVID-19 outcomes based on household income? Our aim is to examine the relationships between these predictors and outcomes in specified geographic areas across New York City.

Data Sources and Cleaning

Data Sources

Integrated Public Use Microdata Series (IPUMS USA)

The Integrated Public Use Microdata Series (IPUMS USA) consists of individual-level data from samples of the US population drawn from the American Community Surveys (ACS) of 2000 - present as well as from fifteen federal censuses from 1850 to 2010. Each record in IPUMS is a person with numerically coded characteristics and “weight” variables indicating how many persons in the population are represented by each record. Samples were created at different times by different investigators, which lead to a variety of documentation conventions. However, IPUMS applies consistent coding and documentation across records to allow for effective analysis over time. A data extraction system exists to allow users to pull particular samples and variables from IPUMS. This project uses demographic and macroeconomic data from the American Community Survey (ACS) 2019 five-year estimate via IPUMS.

While data from IPUMS is recorded at the individual-level, each interview is coded to a particular Public Use Microdata Area (PUMA) geography where the housing unit was located at the time of interview.

New York City Department of Health and Mental Hygiene (NYC DOHMH)

The New York City Department of Health and Mental Hygiene (NYC DOHMH) is one of the oldest public health agencies in the United States. Among other responsibilities, the DOHMH monitors the spread of infectious disease in NYC. The Department of Health classified the beginning of the COVID-19 pandemic as February 29, 2020, the date of the first laboratory-confirmed case. Since then, the DOHMH has recorded and reported COVID-19 data on a daily, weekly, or monthly basis. These data include cases, hospitalizations, and deaths by borough, modified Zip Code tabulation area (ZCTA), and demographic factors. As NYC has administered vaccinations for COVID-19, these data have been recorded and made available by borough, ZCTA, and demography. This project uses COVID-19 hospitalization rates, death rates, and vaccination rates by ZCTA in NYC.

Baruch College, City University of New York - Geoportal

The Baruch Geoportal, maintained by the Newman Library at Baruch College, is a repository of geospatial resources including tabular data sets, tutorials, maps, and crosswalks. This project uses a crosswalk data set from Baruch Geoportal to apportion NYC ZCTAs to PUMAs, which allows PUMA-coded data from IPUMS to be analyzed alongside COVID-19 outcome data from DOHMH.

Data Cleaning

Pulling Data

As mentioned above, monthly outcome data were obtained from the NYC DOHMH with data reported at the ZCTA-level geography. First, these data were summed over the time interval March 2020 - ### to obtain one cumulative incidence measure per ZCTA. However, the predictor variables from IPUMS were coded to the PUMA-level geography. The first step in the cleaning process was to convert these data into a common geography to facilitate further analysis. The Baruch ZCTA-PUMA crosswalk data set was used in this data conversion. Below is a brief excerpt:

# Read in ZCTA/PUMA crosswalk
read_csv("./data/zcta_puma_cross.csv") %>% 
  head() %>% 
  knitr::kable()

zcta10	stateco	alloc	puma10	pumaname	pop2010	per_in_puma	per_of_puma
10451	36005	x	3710	NYC-Bronx Community District 1 & 2–Hunts Point, Longwood & Melrose	22027	0.482	0.141
10451	36005	NA	3708	NYC-Bronx Community District 4–Concourse, Highbridge & Mount Eden	21002	0.459	0.151
10451	36005	NA	3705	NYC-Bronx Community District 3 & 6–Belmont, Crotona Park East & East Tremont	2684	0.059	0.017
10452	36005	x	3708	NYC-Bronx Community District 4–Concourse, Highbridge & Mount Eden	71729	0.952	0.515
10452	36005	NA	3707	NYC-Bronx Community District 5–Morris Heights, Fordham South & Mount Hope	3642	0.048	0.027
10453	36005	x	3707	NYC-Bronx Community District 5–Morris Heights, Fordham South & Mount Hope	77074	0.984	0.574

The following columns were used to convert ZCTA-level outcome data to PUMA-level data:

• ‘zcta10’ - ZCTA unique identifier

• ‘puma10’ - PUMA unique identifier

• ‘per_in_puma’ - percentage of the specified ZCTA that is located within the specified PUMA

• ‘per_of_puma’ - percentage of the specified PUMA that is occupied by the specified ZCTA

The following shows the mathematical expression used to convert from ZCTA-level outcome data to PUMA-level outcome data:

\[ \sum_{i = 1}^{n} \text{zcta_outcome_data}_{i} \cdot \text{per_in_puma}_{i} \cdot \text{per_of_puma}_{i} = \text{puma_outcome_data} \]

This resulted in one cumulative incidence measure per PUMA (per 100,000 people for hospitalizations and deaths, a percentage for vaccinations).

The demographic dataset from IPUMS originally contained over 350,000 interviews from the NYC area, each coded to a PUMA and given a ‘perwt’ - person weight and ‘hhwt’- household weight. First, predictor variables were renamed and recoded according to the data dictionary (link to data dictionary) such that the following predictor variables were obtained for each interview along with ‘borough’ and ‘puma’ coding:

• ‘rent’: monthly rent (numeric)
• ‘household_income’: annual household income (numeric)
• ‘on_foodstamps’: whether a person is on food stamps (binary)
• ‘has_broadband’: whether a person has broadband internet (binary)
• ‘family_size’: number of individuals in family, including this individual (numeric)
• ‘num_children’: number of children in family (numeric)
• ‘sex’: sex of individual (binary)
• ‘age’: age of individual (numeric)
• ‘race’: race of individual (categorical factor)
• ‘birthplace’: whether this person was born in US or elsewhere (categorical factor)
• ‘US_citizen’: whether this person is a US citizen (categorical factor)
• ‘language’: primary language spoken at home (categorical factor)
• ‘education’: highest level of education obtained (categorical factor)
• ‘employment’: current employment status (categorical factor)
• ‘health_insurance’: type of insurance (public or private), if any (categorical factor)
• ‘personal_income’: annual personal income (numeric)
• ‘on_welfare’: whether person is on welfare (binary)
• ‘poverty_threshold’: whether the person is above or below the poverty line (binary)
• ‘work_transport’: most commonly used method of transportation to work (categorical factor)

# Cleaning
jimzip <- function(csv_file, path) {
  # create full path to csv file
  full_csv <- paste0(path, "/", csv_file)
  # append ".zip" to csv file
  zip_file <- paste0(full_csv, ".zip")
  # unzip file
  unzip(zip_file)
  # read csv
  data_extract <- read_csv(csv_file)
  # be sure to remove file once unzipped (it will live in working directory)
  on.exit(file.remove(csv_file))
  # output data
  data_extract
}

# Apply function to filtered census data CSV
census_data <- jimzip("census_filtered.csv", "./data")

# Merging the Outcome Data

# Read in PUMA outcomes data
health_data <-
  read_csv("./data/outcome_puma.csv")

# Merge census data with PUMA outcomes data
merged_data <- merge(census_data, health_data, by = "puma")

# Deprecate census data alone
rm(census_data)

## Cleaning the Data

# Clean the merged census and outcomes data
# Each row represents one 
cleaned_data = 
  merged_data %>% 
  # Remove variables less useful for analysis or redundant (high probability of collinearity with remaining variables)
  select(-serial, -cluster, -strata, -multyear, -ancestr1, -ancestr2, -labforce, -occ, -ind, -incwage, -occscore, -pwpuma00, -ftotinc, -hcovpub) %>% 
  # Remove duplicate rows, if any
  distinct() %>% 
  # Rename variables
  rename(
    borough = countyfip,
    has_broadband = cihispeed,
    birthplace = bpl,
    education = educd,
    employment = empstat,
    personal_income = inctot,
    work_transport = tranwork,
    household_income = hhincome,
    on_foodstamps = foodstmp,
    family_size = famsize,
    num_children = nchild,
    US_citizen = citizen,
    puma_vacc_rate = puma_vacc_per,
    on_welfare = incwelfr,
    poverty_threshold = poverty
  ) %>% 
  # Recode variables according to data dictionary
  mutate(
    # Researched mapping for county
    borough = recode(
      borough,
      "5" = "Bronx",
      "47" = "Brooklyn",
      "61" = "Manhattan",
      "81" = "Queens",
      "85" = "Staten Island"
    ),
    rent = ifelse(
      rent == 9999, 0,
      rent
    ),
    household_income = ifelse(
      household_income %in% c(9999998,9999999), NA,
      household_income
    ),
    on_foodstamps = recode(
      on_foodstamps,
      "1" = "No",
      "2" = "Yes"
    ),
    has_broadband = case_when(
      has_broadband == "20" ~ "No",
      has_broadband != "20" ~ "Yes"
    ),
    sex = recode(
      sex,
      "1" = "Male",
      "2" = "Female"
    ),
    # Collapse Hispanic observation into race observation
    race = case_when(
      race == "1" ~ "White",
      race == "2" ~ "Black",
      race == "3" ~ "American Indian",
      race %in% c(4,5,6) ~ "Asian and Pacific Islander",
      race == 7 & hispan %in% c(1,2,3,4) ~ "Hispanic",
      race == 7 & hispan %in% c(0,9) ~ "Other",
      race %in% c(8,9) ~ "2+ races"
    ),
    birthplace = case_when(
      birthplace %in% 1:120 ~"US",
      birthplace %in% 121:950 ~ "Non-US",
      birthplace == 999 ~"Unknown"
    ),
    US_citizen = case_when(
      US_citizen %in% c(1,2) ~ "Yes",
      US_citizen %in% 3:8 ~"No",
      US_citizen %in% c(0,9) ~ "Unknown"
    ),
    # Chose languages based on highest frequency observed
    language = case_when(
      language == "1" ~ "English",
      language == "12" ~ "Spanish",
      language == "43" ~ "Chinese",
      language == "0" ~ "Unknown",
      language == "31" ~ "Hindi",
      !language %in% c(1,12,43,0,31) ~ "Other"
    ),
    # Collapse multiple health insurance variables into single variable
    health_insurance = case_when(
      hcovany == 1 ~ "None",
      hcovany == 2 && hcovpriv == 2 ~ "Private",
      hcovany == 2 && hcovpriv == 1 ~ "Public"
    ),
    education = case_when(
      education %in% 2:61 ~ "Less Than HS Graduate",
      education %in% 62:64 ~ "HS Graduate",
      education %in% 65:100 ~ "Some College",
      education %in% 110:113 ~ "Some College",
      education == 101 ~ "Bachelor's Degree",
      education %in% 114:116 ~ "Post-Graduate Degree",
      education %in% c(0,1,999) ~ "Unknown"
    ),
    employment = case_when(
      employment %in% c(0,3) ~ "Not in labor force",
      employment == 1 ~ "Employed",
      employment == 2 ~ "Unemployed"
    ),
    personal_income = ifelse(
      personal_income %in% c(9999998,9999999), NA,
      personal_income
    ),
    household_income = ifelse(
      household_income %in% c(9999998,9999999), NA,
      household_income
    ),
    on_welfare = case_when(
      on_welfare > 0 ~ "Yes",
      on_welfare == 0 ~ "No"
    ), 
    poverty_threshold = case_when(
      poverty_threshold >= 100 ~ "Above",
      poverty_threshold < 100 ~ "Below"
    ),
    work_transport = case_when(
      work_transport %in% c(31:37, 39) ~ "Public Transit",
      work_transport %in% c(10:20, 38) ~ "Private Vehicle",
      work_transport == 50 ~ "Bicycle",
      work_transport == 60 ~ "Walking",
      work_transport == 80 ~ "Worked From Home",
      work_transport %in% c(0, 70) ~ "Other"
    )
  ) %>% 
  # Eliminate columns no longer needed after transformation
  select(-hispan, -hcovany, -hcovpriv) %>% 
  # Relocate new columns
  relocate(health_insurance, .before = personal_income) %>% 
  relocate(poverty_threshold, .before = work_transport) %>% 
  relocate(on_welfare, .before = poverty_threshold) %>% 
  relocate(perwt, .before = hhwt) %>% 
  # Create factor variables where applicable
  mutate(across(.cols = c(puma, borough, on_foodstamps, has_broadband, sex, race, birthplace, US_citizen, language, health_insurance, education, employment, on_welfare, poverty_threshold, work_transport), as.factor)) %>% 
  # Ensure consistent use of percentages
  mutate(
    puma_death_rate = puma_death_rate / 100,
    puma_hosp_rate = puma_hosp_rate / 100
  )

# View first few rows
cleaned_data %>% 
  head() %>% 
  knitr::kable()

puma	perwt	hhwt	borough	rent	household_income	on_foodstamps	has_broadband	family_size	num_children	sex	age	race	birthplace	US_citizen	language	education	employment	health_insurance	personal_income	on_welfare	poverty_threshold	work_transport	puma_death_rate	puma_hosp_rate	puma_vacc_rate
3701	18	25	Bronx	0	166870	No	No	2	0	Male	58	White	Non-US	Yes	English	Post-Graduate Degree	Employed	Private	83435	No	Above	Public Transit	3.982366	10.64624	55.79213
3701	22	22	Bronx	1018	123192	No	Yes	2	0	Male	52	Black	Non-US	Yes	Other	Some College	Employed	Private	107920	No	Above	Private Vehicle	3.982366	10.64624	55.79213
3701	16	17	Bronx	2000	125000	No	Yes	1	0	Female	59	White	US	Unknown	Spanish	Some College	Employed	Private	125000	No	Above	Public Transit	3.982366	10.64624	55.79213
3701	4	6	Bronx	0	140588	Yes	Yes	6	3	Male	64	Asian and Pacific Islander	Non-US	Yes	Chinese	Post-Graduate Degree	Not in labor force	Private	11264	No	Above	Other	3.982366	10.64624	55.79213
3701	20	19	Bronx	1058	52876	No	Yes	2	1	Male	44	White	Non-US	Yes	Spanish	Some College	Employed	Private	32373	No	Above	Public Transit	3.982366	10.64624	55.79213
3701	9	9	Bronx	0	26101	No	Yes	1	0	Female	64	White	US	Unknown	English	Post-Graduate Degree	Employed	Private	26101	No	Above	Private Vehicle	3.982366	10.64624	55.79213

After cleaning variable names the 350,000+ interviews were summarized to the PUMA-level based on ‘perwt’ and ‘hhwt’. For each interview, the ‘perwt’ value describes the number of persons in the coded geographic area (PUMA) for which the interview is representative. For example, a ‘perwt’ of 34 indicates that there are 34 persons in the PUMA that share the same characteristics as described in the interview data (e.g., similar income, race, family size, etc.). The same is true of the ‘hhwt’ value for households in the coded PUMA. Therefore, the ‘perwt’ and ‘hhwt’ of each interview can be used to aggregate interview-level data to PUMA-level data as follows:

# Example data frame with weightings for summary stats over each PUMA
nyc_puma_summary = cleaned_data %>% 
  # Note: do we need to filter to one individual per household for household weightings?
  group_by(puma) %>%
  summarize(
    total_people = sum(perwt),
    median_household_income = weighted.median(household_income, hhwt, na.rm = TRUE),
    perc_foodstamps = sum(hhwt[on_foodstamps == "Yes"]) * 100 / sum(hhwt),
    perc_broadband = sum(hhwt[has_broadband == "Yes"]) * 100 / sum(hhwt),
    perc_male = sum(perwt[sex == "Male"]) * 100 / sum(perwt),
    median_age = weighted.median(age, perwt, na.rm = TRUE),
    perc_white = sum(perwt[race == "White"]) * 100 / sum(perwt),
    perc_foreign_born = sum(perwt[birthplace == "Non-US"]) * 100 / sum(perwt),
    perc_citizen = sum(perwt[US_citizen == "Yes"]) * 100 / sum(perwt),
    perc_english = sum(perwt[language == "English"]) * 100 / sum(perwt),
    perc_college = sum(perwt[education %in% c("Some College", "Bachelor's Degree", "Post-Graduate Degree")]) * 100 / sum(perwt),
    perc_unemployed = sum(perwt[employment == "Unemployed"]) * 100 / sum(perwt),
    perc_insured = sum(perwt[health_insurance %in% c("Private", "Public")]) * 100 / sum(perwt),
    median_personal_income = weighted.median(personal_income, perwt, na.rm = TRUE),
    perc_welfare = sum(perwt[on_welfare == "Yes"]) * 100 / sum(perwt),
    perc_poverty = sum(perwt[poverty_threshold == "Below"]) * 100 / sum(perwt),
    perc_public_transit = sum(perwt[work_transport == "Public Transit"]) * 100 / sum(perwt),
    covid_hosp_rate = median(puma_hosp_rate),
    covid_vax_rate = median(puma_vacc_rate),
    covid_death_rate = median(puma_death_rate)
  )

# View first few rows of PUMA-summarized data frame
nyc_puma_summary %>% head() %>% knitr::kable()

puma	total_people	median_household_income	perc_foodstamps	perc_broadband	perc_male	median_age	perc_white	perc_foreign_born	perc_citizen	perc_english	perc_college	perc_unemployed	perc_insured	median_personal_income	perc_welfare	perc_poverty	perc_public_transit	covid_hosp_rate	covid_vax_rate	covid_death_rate
3701	110016	69000	24.49306	89.50725	46.88500	39	46.53050	34.50407	20.26887	41.74120	47.96393	3.449498	93.91725	22357.09	20.21706	22.66943	24.79821	10.646245	55.79213	3.982366
3702	151067	68610	28.24215	82.93904	45.12435	36	14.06925	42.97100	27.86909	66.47183	39.83729	4.534412	92.58276	20859.00	22.08623	18.60036	21.55732	11.782181	47.19203	2.688261
3703	119529	77588	15.90074	86.60915	46.66734	43	41.20088	22.69324	16.91138	58.42432	45.13131	3.577374	94.11273	25030.00	16.73067	16.28140	19.85292	13.040106	58.33806	4.052719
3704	126664	64662	23.88688	81.56041	47.66311	37	32.72911	37.88685	23.03812	41.10165	40.30664	4.141666	92.33879	20362.00	20.17700	18.97698	23.55681	6.861973	29.38498	2.092428
3705	171016	36500	50.66455	87.59563	46.19509	30	15.45177	33.49043	16.46103	33.31033	28.35290	5.289563	91.41484	11264.00	29.20428	39.26943	23.03995	8.255382	33.17926	2.018467
3706	131986	43490	46.18132	82.15610	48.26724	32	19.37099	46.80496	20.58855	20.86812	29.15536	5.606655	89.18219	15000.00	25.09812	32.16402	28.97883	7.723878	32.95661	1.812561

This cleaned and aggregated data set has 55 rows, one for each PUMA, and is the basis of the exploratory analysis that follows.

Exploratory Analysis

Overview of Outcome Variables

Ultimately, we ended the data cleaning process with two data sets at different levels of aggregation: one at the census interview level, and another at the PUMA level. Most of our exploratory analysis focused on evaluating predictors and outcomes by PUMA, although the interview-level data was still helpful for us to determine outcome disparities across predictors city-wide.

We began by seeking a better understanding of how each of our three key outcomes – hospitalization rate, death rate, and vaccination rate – differ by PUMA. When PUMAs are ranked from lowest outcome rate to highest outcome rate, and colored by borough, we find the following: * Hospitalization rate ranges from nearly 4% to nearly 20%, with the plurality of high hospitalization rates occurring in Queens PUMAs and the plurality of low hospitalization rates occurring in Manhattan and Brooklyn PUMAs * Death rate ranges from <1% to over 6%, with the plurality of high death rates occurring in Queens PUMAs and the plurality of low death rates occurring in Manhattan and Brooklyn PUMAs * Vaccination rate ranges from nearly X% to over 100% (due to migrations between PUMAs), with all of the highest vaccination rates occurring in Manhattan and Queens, and all of the lowest vaccination rates occurring in Brooklyn and the Bronx

Although our regression modeling explores the relationship between particular variable pairings more fully to check for collinearity, we also were interested in observing how associated our key outcome variables were, and found that hospitalization and death rate were significantly correlated, whereas vaccination had limited correlation with both hospitalization (0.187) and death (0.075) at the PUMA level. Interestingly, the correlation between our key outcome variables was effectively modified by borough; for example, vaccination and hospitalization were significantly correlated in the Bronx (0.930), whereas hospitalization and death were not significantly correlated in Staten Island (0.526).

Outcomes by Borough

After exploring outcomes at the PUMA level, we were keen to dive more deeply into disparities by borough. Beyond simply confirming with boxplots the distribution of key outcomes across PUMAs in a given borough (e.g. hospitalization and death distributed towards higher rates in Queens and Bronx PUMAs, vaccination distributed towards higher rates in Queens and Manhattan), we were also curious to see what would happen if we took the median city-wide PUMA for each outcome, and binarily divided the PUMAs in each borough into those above the city-wide median and those below it. Although we’re working with only 55 PUMAs, which makes our borough percentages highly sensitive to any given PUMA given small sample size, we find – to take one example, that ~79% of PUMAs in Queens are above the city-wide median PUMA on death rate, but ~86% of PUMAs in Queens are above the city-wide median PUMA on vaccination rate.

% of PUMAs in Each Borough Above Citywide PUMA Median

Borough	Total PUMAs	% Above Hosp Median	% Above Death Median	% Above Vax Median
Bronx	10	70.0	50.0	20.0
Brooklyn	18	22.2	38.9	16.7
Manhattan	10	30.0	30.0	80.0
Queens	14	85.7	78.6	85.7
Staten Island	3	33.3	33.3	66.7

Outcomes by Demographic Combinations

For each unique combination of age group, race, and sex, we wanted to determine which demographic category performed best and worst on each key outcome, and populated the following tables:

# Lowest hospitalization rates
race_age_sex %>% 
  filter(outcome == "hosp_rate") %>% 
  mutate(
    outcome_rate = outcome_rate / 100
  ) %>% 
  arrange(outcome_rate) %>% 
  select(race, age_class, sex, outcome, outcome_rate) %>% 
  head() %>% 
  knitr::kable()

race	age_class	sex	outcome	outcome_rate
White	21-30	Female	hosp_rate	0.0876151
White	31-40	Male	hosp_rate	0.0885909
White	31-40	Female	hosp_rate	0.0890869
White	21-30	Male	hosp_rate	0.0896349
White	41-50	Male	hosp_rate	0.0927537
White	41-50	Female	hosp_rate	0.0934757

# Highest hospitalization rates
race_age_sex %>% 
  filter(outcome == "hosp_rate") %>% 
  mutate(
    outcome_rate = outcome_rate / 100
  ) %>% 
  arrange(desc(outcome_rate)) %>% 
  select(race, age_class, sex, outcome, outcome_rate) %>% 
  head() %>% 
  knitr::kable()

race	age_class	sex	outcome	outcome_rate
American Indian	81-90	Male	hosp_rate	0.1272494
Other	61-70	Male	hosp_rate	0.1216952
Other	11-20	Male	hosp_rate	0.1211757
Other	41-50	Male	hosp_rate	0.1200270
Other	61-70	Female	hosp_rate	0.1185198
Asian and Pacific Islander	91-100	Male	hosp_rate	0.1173874

# Lowest death rates
race_age_sex %>% 
  filter(outcome == "death_rate") %>% 
  mutate(
    outcome_rate = outcome_rate / 100
  ) %>% 
  arrange(outcome_rate) %>% 
  select(race, age_class, sex, outcome, outcome_rate) %>% 
  head() %>% 
  knitr::kable()

race	age_class	sex	outcome	outcome_rate
White	21-30	Female	death_rate	0.0237663
White	31-40	Male	death_rate	0.0242434
White	21-30	Male	death_rate	0.0243574
White	31-40	Female	death_rate	0.0245547
Other	81-90	Male	death_rate	0.0254102
White	41-50	Male	death_rate	0.0256468

# Highest death rates
race_age_sex %>% 
  filter(outcome == "death_rate") %>% 
  mutate(
    outcome_rate = outcome_rate / 100
  ) %>% 
  arrange(desc(outcome_rate)) %>% 
  select(race, age_class, sex, outcome, outcome_rate) %>% 
  head() %>% 
  knitr::kable()

race	age_class	sex	outcome	outcome_rate
2+ races	91-100	Male	death_rate	0.0352503
Asian and Pacific Islander	91-100	Male	death_rate	0.0338679
American Indian	81-90	Male	death_rate	0.0324616
Other	11-20	Male	death_rate	0.0322860
Other	41-50	Male	death_rate	0.0322078
Other	71-80	Male	death_rate	0.0320242

# Lowest vax rates
race_age_sex %>% 
  filter(outcome == "vax_rate") %>% 
  mutate(
    outcome_rate = outcome_rate
  ) %>% 
  arrange(outcome_rate) %>% 
  select(race, age_class, sex, outcome, outcome_rate) %>% 
  head() %>% 
  knitr::kable()

race	age_class	sex	outcome	outcome_rate
American Indian	71-80	Male	vax_rate	49.32433
Black	11-20	Female	vax_rate	49.35445
Black	<11	Male	vax_rate	49.47578
Black	11-20	Male	vax_rate	49.48017
Black	31-40	Female	vax_rate	49.49496
Black	<11	Female	vax_rate	49.51926

# Highest vax rates
race_age_sex %>% 
  filter(outcome == "vax_rate") %>% 
  mutate(
    outcome_rate = outcome_rate
  ) %>% 
  arrange(desc(outcome_rate)) %>% 
  select(race, age_class, sex, outcome, outcome_rate) %>% 
  head() %>% 
  knitr::kable()

race	age_class	sex	outcome	outcome_rate
Asian and Pacific Islander	91-100	Female	vax_rate	66.13596
Asian and Pacific Islander	71-80	Female	vax_rate	65.89982
Asian and Pacific Islander	71-80	Male	vax_rate	65.73426
Asian and Pacific Islander	31-40	Male	vax_rate	65.61553
Asian and Pacific Islander	31-40	Female	vax_rate	65.57662
2+ races	81-90	Male	vax_rate	65.47910

Overall, hospitalization and death rates were lowest (best) among white males and females under age 30, whereas vaccination rates were highest (best) among Asian and Pacific Islander males and females. Older American Indian individuals, along with younger and middle-aged Black individuals, tended to have the lowest vaccination rates, while mixed race, American Indian, and “other” racial groups tended to have higher hospitalization and death rates.

Associations Between Individual Predictors and Outcomes

After exploring disparities in key outcomes across PUMAs and boroughs, we turn towards our large set of predictors, and begin by trying to determine which predictors to focus on using a correlation matrix (with outcomes). In the plot below, we include text only on those tiles that are highly significant, with p < 0.01.

Interestingly, we find: * The variables highly positively correlated with hospitalization rate at the PUMA level are percent US citizens and percent foreign born; the variables highly negatively correlated with hospitalization rate at the PUMA level are percent white, percent using public transit to get to work, percent with health insurance, percent English-speaking at home, percent with college education, percent with broadband access, and median personal and household incomes. * The variables highly positively correlated with death rate at the PUMA level, are percent US citizens and percent foreign born; the variables highly negatively correlated with death rate at the PUMA level are percent using public transit to get to work, percent with health insurance, percent college educated, and median personal and household incomes. * The variables highly positively correlated with vaccination rate at the PUMA level are percent white, percent male, percent college educated, percent with broadband access, median age, and median personal and household incomes; the variables highly negatively correlated with vaccination rate at the PUMA level are percent on welfare, percent unemployed, percent below the poverty threshold, and percent on food stamps

All in all, there are a couple of interesting trends observed in this correlation matrix. First, income seems strongly associated with all three outcome variables. In addition, the variables strongly associated with hospitalization rate also tend to be strongly associated with death rate, which is not much of a surprise given the high correlation already observed between hospitalization and death rate across PUMAs. Finally, we note that many signifiers of socioeconomic status – including poverty level, welfare, unemployment, and food stamp utilization – seem highly correlated with vaccination, but not with hospitalization and death. Given that vaccination is a more “active” outcome (requiring deliberate action) here than hospitalization or death, which are both the result of (in all likelihood) “passive” or indeliberate transmission, the association of socioeconomic factors with vaccination begin to indicate the potential impact from significant structural inequalities at play, hindering healthcare access among the poor.

We then selected each of the four variables with highest correlation (positive or negative) to each predictor, excluding obvious redundancies (like personal income and household income), and explored specific association trends between predictor and outcome, colored by borough.

Beyond the predictors significantly associated with each outcome, we wanted to focus as well on how outcomes varied by levels of key socioeconomic variables – namely, race, age group, and sex. Because we lack individual outcome data (i.e. each census observation within a given PUMA has the same PUMA-level hospitalization, death, and vaccination rate), we assumed for this analysis that all persons in a given PUMA had equal likelihood of a particular outcome (hospitalization, death, or vaccination) being true, with the likelihood corresponding to the PUMA outcome rate.

Some key findings include: * Males and females appear similar on each outcome * Hospitalization and death rates tend to be higher after middle age compared to those below middle age, whereas vaccination rate shows a general increase with each age group * In general, white individuals have a lower likelihood of hospitalization and death, but a higher likelihood – along with Asian and Pacific Islanders – of vaccination, whereas other groups of color and Native Americans seem to have higher hospitalization and death rates, but lower vaccination rates

Similarly, we examined how key outcomes varied across categories of a few seemingly important predictor variables for each outcome observed in our correlation matrix:

Again, there were a few interesting findings here, such as: * We observe a monotonic decrease in hospitalization and death rate as household income increases, but a monotonic increase in vaccination rate as household income increases as well * Individuals with public health insurance tend to perform similarly on key outcomes to those with no health insurance at all, with both groups worse than those who have private health insurance * Individuals with college and graduate education tend to perform better on key outcomes than those without any college education * Those with unknown citizenship status, which may signify being “undocumented,” tend to have lower death rates – perhaps indicative of underreporting due to fear of immigration control / policing, i.e. attention on the person or family * As already noted, those on welfare and foodstamps, as well as unemployed, are significantly less likely to be vaccinated against COVID-19

Associations Between Predictors and Outcomes by Borough

To build on the work above, we wanted to observe disparities within boroughs, knowing that different boroughs have different demographic compositions and that the ideal visualizations would allow us to understand how outcomes vary conditioned on borough demographic composition. Each of the following visualizations has three panels: number of people with outcome, categorized by borough and colored by predictor level; % of people with outcome in each borough, colored by predictor level, compared to the overall composition of the borough by predictor level; and percent with outcome variable, in each borough, plotted by level of predictor.

The most interesting finding here is that Manhattan seems to have the most significant racial disparities on hospitalization rate and death rate, along with age disparities on hospitalization rate, and racial and age disparities in vaccination rate. In general, the level of inequality on key outcomes across demographics in Manhattan tends to be higher than in other boroughs.

Another set of data visualizations that shows how different outcome rates vary within boroughs across levels of a key demographic predictor (age group, sex, race) is included below.

Regression

Let \(S\) denote the set of PUMAs in NYC. We consider the latent variable model \[ y_s = \xi_s' \beta + \varepsilon_s \] for each \(s \in S\), where \(\xi_s\) a vector of PUMA-level means of data from the census. There are two challenges in considering such a model: (1) we know historically that NYC neighborhoods, particularly those within boroughs, are subject to spatial correlation; and (2) because the census data is recorded at the interview level, we do not observe the group-level means \(\xi_s\).

In order to address (1), we employ heteroscedasticity-robust White standard errors to deal with the potential threat of spatial correlation. We find that all of our coefficient estimates retain their significance under the adjusted standard errors, and hence we leave this check on robustness to the appendix.

More interesting is the challenge presented in (2). For each \(s \in S\), suppose we observe \(i \in \{ 1, \ldots, n_s \}\) individual-level interviews. It is natural to consider the group mean \[ \bar{X}_s \equiv \frac{1}{n_s} \sum_{i = 1}^{n_s} X_{is}. \] However, as shown in Croon and Veldhoven (2007), it is generally the case that using the observed group mean \(\bar{X}_s\) as an estimator of \(\xi_s\) will lead to biased regression coefficients. Thus, we address (2) by following the procedure outlined by Croon and Veldhoven to re-weight our group means and obtain adjusted group means \(\tilde{X}_s\). In particular, let $ _{}$ and \(\hat{\Sigma}_{\nu \nu}\) denote the usual ANOVA estimates of the between- and within-group variation matrices, respectively. The adjusted group means are then given by \[ \tilde{X}_s \equiv \bar{X}' (I - W_s) + \bar{X}_s' W_s, \quad \text{where} \] \[ W_s \equiv \left( \hat{\Sigma}_{\xi \xi} + \hat{\Sigma}_{\nu \nu} / n_s \right)^{-1} \hat{\Sigma}_{\xi \xi} \] and \(I\) denotes the identity matrix.

TODO: Output

Predictive Risk Scoring & Clustering

Risk Scoring

Following our regression work, we decided to make our insights more actionable by developing a novel scoring method capable of indicating whether a PUMA is at relatively lower or higher risk of achieving some COVID-19-related outcome. To demonstrate the method, we developed a risk score for whether a PUMA is likely to have achieved or not achieved a vaccination rate of 70% among residents, corresponding to the level of population immunity generally considered requisite to “halt the pandemic.” That said, our method is applicable to other outcomes as well, and one might imagine using it to score a given PUMA on the possibility of a hospitalization rate above X%, or a death rate above Y%. We only chose to begin with vaccination rate given our inability to develop a linear regression for this particular outcome, as opposed to hospitalization and death rates.

The risk scoring method we developed is predicated on (regularized, lasso) logistic regression, used most often for classification tasks because predictions can be interpreted as class probabilities. Regularization further prevents overfitting of the model. After defining our outcome as 1 for below 70% vaccination and 0 for equal to or above 70% vaccination, we converted our set of predictors to matrix form, and then trained a glmnet model on our training data using 5-fold cross-validation repeated 100 times given the large number of predictors compared to our mere 55 PUMA samples, and because we were interested in predicting the risk score of vaccination rate for each PUMA in our data set. Through our lasso regression, we found an optimal lambda tuning parameter of 0.0102, and generated a model prediction accuracy of 0.886 (~87%). Generally, however, obtaining the kappa value averaged over the simulated confusion matrices is a more useful metric for prediction given unbalanced classes (of our 55 PUMAs, 41 achieve vaccination rate >= 70%, and only 14 do not); Our optimal model’s averaged kappa was 0.63, which is considered reasonably decent, but again suggests that the limited number of in-sample data points may result in model overfitting.

# 1 indicates BELOW 70% vaccination rate
logistic_df = nyc_puma_summary %>% 
  mutate(
    below_herd_vax = as.factor(ifelse(covid_vax_rate >= 70, 0, 1))
  ) %>% 
  select(-puma, -total_people, -covid_hosp_rate, -covid_death_rate, -covid_vax_rate)

# Define predictors matrix
x = model.matrix(below_herd_vax ~ ., logistic_df)[,-1]

# Define outcomes
y = logistic_df$below_herd_vax

library(caret) # Note: new libraries are loaded here due to potential function masking from the `caret` library
library(mlbench)

set.seed(777)
vax_cv <- trainControl(method = "repeatedcv", number = 5, repeats = 100, 
                       savePredictions = T
                       )

# Goal is to find optimal lambda
lasso_model <- train(below_herd_vax ~ ., data = logistic_df,
                     method = "glmnet",
                     trControl = vax_cv,
                     tuneGrid = expand.grid(
                       .alpha = 1,
                       .lambda = seq(0.0001, 1, length = 100)),
                     family = "binomial")

coef <- coef(lasso_model$finalModel, lasso_model$bestTune$lambda)

sub_lasso <-
  subset(lasso_model$pred, lasso_model$pred$lambda == lasso_model$bestTune$lambda)

caret::confusionMatrix(table(sub_lasso$pred, sub_lasso$obs))

## Confusion Matrix and Statistics
## 
##    
##        0    1
##   0  731  258
##   1  369 4142
##                                           
##                Accuracy : 0.886           
##                  95% CI : (0.8773, 0.8943)
##     No Information Rate : 0.8             
##     P-Value [Acc > NIR] : < 2.2e-16       
##                                           
##                   Kappa : 0.6297          
##                                           
##  Mcnemar's Test P-Value : 1.118e-05       
##                                           
##             Sensitivity : 0.6645          
##             Specificity : 0.9414          
##          Pos Pred Value : 0.7391          
##          Neg Pred Value : 0.9182          
##              Prevalence : 0.2000          
##          Detection Rate : 0.1329          
##    Detection Prevalence : 0.1798          
##       Balanced Accuracy : 0.8030          
##                                           
##        'Positive' Class : 0               
## 

Notably, feature selection from our lasso regression discovered that the most important predictors of risk for sub-70% vaccination were insurance composition, employment composition, poverty composition, and welfare composition in a given PUMA – largely aligned with key correlates of vaccination noted in our exploratory analysis.

lambda  <- seq(0.0001, 1, length = 100)

lambda_opt = lasso_model$bestTune$lambda

result_plot <- broom::tidy(lasso_model$finalModel) %>% 
  select(term, lambda, estimate) %>% 
  complete(term, lambda, fill = list(estimate = 0) ) %>% 
  filter(term != "(Intercept)") %>% 
  ggplot(aes(x = log(lambda, 10), y = estimate, group = term, color = term)) + 
  geom_path() + 
  geom_vline(xintercept = log(lambda_opt, 10), color = "blue", size = 1.2) +
  theme(legend.position = "none") +
  labs(y = "Coefficient Estimate", title = "Coefficient Estimates for Varying Values of Lambda")

result_plot

Again, we wanted to move beyond binary classification to develop a risk score. Generally, in logistic regression, when a data point is predicted with probability > 0.5 to be a “1,” the model classifies it as a 1, and otherwise as a 0. We obtained risk scores not only by classifying PUMAs as above or below 70% vaccination rate using our prediction model, but by obtaining the exact probability of a given data point being a 1. For instance, if a PUMA has an 85% chance of being below 70% vaccination rate according to our classifier, its risk score would be 85, even though our model would binarily predict it to be a “1” rather than a “0.”

lambda <- lasso_model$bestTune$lambda
lasso_fit = glmnet(x, y, lambda = lambda, family = "binomial")
risk_predictions = (round((predict(lasso_fit, x, type = "response"))*100, 1))

puma <- nyc_puma_summary %>% 
  select(puma)

vax <- logistic_df %>% 
  select(below_herd_vax)

risk_prediction <- 
  bind_cols(puma, vax, as.vector(risk_predictions)) %>%
  rename(risk_prediciton = ...3)

risk_prediction %>%
  mutate(puma = fct_reorder(puma, risk_prediciton, .desc = TRUE)) %>%
  ggplot(aes(x = puma, y = risk_prediciton, fill = below_herd_vax)) + 
  geom_bar(stat  = "identity") + 
  geom_hline(yintercept = 50, linetype = "dashed", color = "red") +
  theme(axis.text.x = element_text(angle = 90, vjust = 0.5, hjust = 1)) +
  labs(title = "Predicting Risk Score of Vaccination Rate across PUMA",
       x = "PUMA", y = "Risk Score") + 
  scale_fill_manual(values = c("yellow", "purple"), labels = c("Below 70%", "Above 70%"))

Clustering

We were also curious how statistical learning techniques would cluster our PUMAs based on predictors, and how those clusters might correspond to performance on key outcomes. We separated our data into a tibble of predictors only and a tibble of outcomes only, then fit three clusters – just to try it – on our predictors alone. We proceeded to plot each PUMA on hospitalization rate vs vaccination rate (choosing to forego death rate, in this case, given its collinearity and likely redundancy of hospitalization rate), then colored each data point by predicted clustering.

# Define tibble of predictors only
predictors = nyc_puma_summary %>% 
  select(-puma, -total_people, -covid_hosp_rate, -covid_vax_rate, -covid_death_rate)

# Define tibble of outcomes only
outcomes = nyc_puma_summary %>% 
  select(covid_hosp_rate, covid_death_rate, covid_vax_rate)

# Define tibble of pumas only
pumas = nyc_puma_summary %>% 
  select(puma)

# Fit 3 clusters on predictors
kmeans_fit = 
  kmeans(x = predictors, centers = 3)

# Add clusters to data frame of predictors and bind with PUMA and outcomes data
predictors = 
  broom::augment(kmeans_fit, predictors)

# Bind columns
full_df = cbind(pumas, outcomes, predictors)

# Summary df
summary_df = full_df %>% 
  group_by(.cluster) %>% 
  summarize(
    median_hosp = median(covid_hosp_rate),
    median_death = median(covid_death_rate),
    median_vax = median(covid_vax_rate)
  )

# Plot predictor clusters against outcomes
# Example: try hospitalization vs vaccination
ggplot(data = full_df, aes(x = covid_hosp_rate, y = covid_vax_rate, color = .cluster)) + 
  geom_point() + 
  geom_point(data = summary_df, aes(x = median_hosp, y = median_vax), color = "black", size = 4) +
  geom_point(data = summary_df, aes(x = median_hosp, y = median_vax, color = .cluster), size = 2.75) +
  labs(x = "COVID Hospitalization Rate", y = "COVID Vaccination Rate", title = "COVID Hospitalization vs Vaccination Rates for each PUMA", color = "Cluster")

Generally, our three clusters included: * One cluster with relatively low hospitalization rate (~5%) and relatively high vaccination rate (~75%) * Two clusters with relatively identical average hospitalization rate (~10%), but one with substantially higher vaccination rate (nearly 60%) than the other (nearly 50%)

For fun, we also evaluated Euclidean distance between our observed PUMAs, and alternatively mapped PUMAs onto their respective clusters after reducing our predictors to two key (principal) component dimensions.

# Scale predictors
for_clustering = predictors %>% 
  select(-.cluster) %>% 
  na.omit() %>% 
  scale()

# Evaluate Euclidean distances between observations
distance = get_dist(for_clustering)
fviz_dist(distance, gradient = list(low = "#00AFBB", mid = "white", high = "#FC4E07"))

# Cluster with three centers
k_scaled = kmeans(for_clustering, centers = 3)

# Visualize cluster plot with reduction to two dimensions
fviz_cluster(k_scaled, data = for_clustering)

# Bind with outcomes and color clusters
full_df = for_clustering %>% 
  as_tibble() %>% 
  cbind(outcomes, pumas) %>% 
  mutate(
    cluster = k_scaled$cluster
  )

summary_df = full_df %>% 
  group_by(cluster) %>% 
  summarize(
    median_hosp = median(covid_hosp_rate),
    median_death = median(covid_death_rate),
    median_vax = median(covid_vax_rate)
  )

ggplot(data = full_df, aes(x = covid_hosp_rate, y = covid_vax_rate, color = factor(cluster))) + 
  geom_point() + 
  geom_point(data = summary_df, aes(x = median_hosp, y = median_vax), color = "black", size = 4) +
  geom_point(data = summary_df, aes(x = median_hosp, y = median_vax, color = factor(cluster)), size = 2.75) +
  labs(x = "COVID Hospitalization Rate", y = "COVID Vaccination Rate", title = "COVID Hospitalization vs Vaccination Rates for each PUMA", color = "Cluster")

Because we settled on setting the number of clusters at three relatively arbitrarily, we decided to evaluate the clustering quality using both WSS, silhouette, and gap methods.

# Check where elbow occurs using WSS method
fviz_nbclust(for_clustering, kmeans, method = "wss")

# Check for optimal number of clusters using silhouette method
fviz_nbclust(for_clustering, kmeans, method = "silhouette")

# Check number of clusters that minimize gap statistic
gap_stat = clusGap(for_clustering, FUN = kmeans, nstart = 25, K.max = 20, B = 50)
fviz_gap_stat(gap_stat)

The elbow in our WSS plot indicates that three clusters may be optimal, whereas the silhouette plot shows an average silhouette width optimized at two clusters. Finally, the gap plot shows that clustering is actually optimized when the number of clusters equals 1 – i.e. when no clustering occurs. The relative lack of concordance between these assessments of clustering quality is no surprise given the fact that our model is fit on only 55 predictors. For completeness, we re-modeled our clustering of predictors with only k = 2 clusters, and again tried to visualize where these clusters of PUMAs were distributed on the hospitalization/vaccination rate axes:

# Scale predictors
for_clustering = predictors %>% 
  select(-.cluster) %>% 
  na.omit() %>% 
  scale()

# Evaluate Euclidean distances between observations
distance = get_dist(for_clustering)
fviz_dist(distance, gradient = list(low = "#00AFBB", mid = "white", high = "#FC4E07"))

# Cluster with two centers
k_scaled2 = kmeans(for_clustering, centers = 2)

# Visualize cluster plot with reduction to two dimensions
fviz_cluster(k_scaled2, data = for_clustering)

# Bind with outcomes and color clusters
full_df = for_clustering %>% 
  as_tibble() %>% 
  cbind(outcomes, pumas) %>% 
  mutate(
    cluster = k_scaled2$cluster
  )

summary_df = full_df %>% 
  group_by(cluster) %>% 
  summarize(
    median_hosp = median(covid_hosp_rate),
    median_death = median(covid_death_rate),
    median_vax = median(covid_vax_rate)
  )

ggplot(data = full_df, aes(x = covid_hosp_rate, y = covid_vax_rate, color = factor(cluster))) + 
  geom_point() + 
  geom_point(data = summary_df, aes(x = median_hosp, y = median_vax), color = "black", size = 4) +
  geom_point(data = summary_df, aes(x = median_hosp, y = median_vax, color = factor(cluster)), size = 2.75) +
  labs(x = "COVID Hospitalization Rate", y = "COVID Vaccination Rate", title = "COVID Hospitalization vs Vaccination Rates for each PUMA", color = "Cluster")

With two clusters, our low hospitalization/high vaccination cluster remains, but our two mid-level hospitalization rate clusters are condensed into one cluster.

Discussion

To do!